Positive solutions to p-Laplacian fractional differential equations with infinite-point boundary value conditions

Han Wang,Suli Liu,Huilai Li

doi:10.1186/s13662-018-1886-2

Han Wang, Suli Liu + Show 1 more

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https://doi.org/10.1186/s13662-018-1886-2

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Journal: Advances in Difference Equations	Publication Date: Nov 20, 2018
Citations: 3	License type: open-access

Affiliation: Jilin University

Abstract

This paper is devoted to an investigation of the multiple positive solutions to a class of infinite-point boundary value problems of nonlinear fractional differential equations coupled with the p-Laplacian operators and infinite-point boundary value conditions. By means of the properties of Green’s function and fixed point theorems, we establish the suitable criteria to guarantee the existence of positive solutions. Finally, an example is given in order to illustrate the main results.

Highlights

With the advance of technology, researchers are not satisfied with the limitations of the integer order calculus anymore; fractional calculus—the expansion and extension of the integer one—is brought into the public
We consider a class of nonlinear fractional differential equations coupled with the p-Laplacian operator and infinite-point boundary value conditions:
To the best of our knowledge, few researchers studied fractional differential equations with p-Laplacian by the Riemann–Liouville derivative; this condition coupled with values at infinite number of points is not covered in the previous situations, and it is more general for the fractional differential equation models

Summary

Introduction

With the advance of technology, researchers are not satisfied with the limitations of the integer order calculus anymore; fractional calculus—the expansion and extension of the integer one—is brought into the public. Wang [8] considered the iterative positive solutions for a class of nonlocal fractional differential equations with nonlocal Hadamard integral and discrete boundary conditions by the monotone iterative method:. Xiping Liu [12, 13] obtained some new results on the existence of positive solutions for the four-point BVP with mixed fractional derivatives and p-Laplacian operator by a new method of lower and upper solutions which is based on the monotone iterative technique:. We consider a class of nonlinear fractional differential equations coupled with the p-Laplacian operator and infinite-point boundary value conditions:. To the best of our knowledge, few researchers studied fractional differential equations with p-Laplacian by the Riemann–Liouville derivative; this condition coupled with values.

Preliminaries

Conclusions